In this paper, a predator-prey model with Holling type-I functional response and multi
state impulsive feedback control is established, where the intensity of pesticide
spraying and the release amount of natural enemies are linearly dependent on the
given threshold in the second impulse. Firstly, the existence of order-1 periodic
solution of the system is investigated by successor functions and Bendixson theorem
of impulsive differential equations, then the stability of periodic solutions is proved by
the analogue of the Poincaré criterion. Furthermore, in order to reduce the actual
total cost and obtain the best economic benefit, the optimal economic threshold is
obtained, which provides the optimal strategy for the practical application. Finally,
numerical simulations for specific examples are carried out to illustrate the feasibility
of the above conclusions.

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• Geometrical analysis and control optimization of a predator-prey model with multi state-dependent impulse